Overlap as function of distance

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SUMMARY

The discussion focuses on calculating the overlap integral between atomic orbitals centered on two different atoms, A and B, as a function of their separation distance. Participants emphasize the need to convert spherical polar coordinates to Cartesian coordinates and consider the impact of molecular distortions. The conversation also explores the use of the Slater wave function, which incorporates both occupied and unoccupied orbitals, and discusses the mathematical approach to restrict overlap calculations to relevant portions of the wave functions.

PREREQUISITES
  • Understanding of spherical harmonics and radial wavefunctions
  • Knowledge of Linear Combination of Atomic Orbitals (LCAO)
  • Familiarity with Slater wave functions
  • Basic concepts of quantum mechanics and wave function overlap
NEXT STEPS
  • Research methods for converting spherical polar coordinates to Cartesian coordinates
  • Learn about the mathematical formulation of the Slater wave function
  • Explore techniques for calculating overlap integrals in quantum chemistry
  • Investigate the impact of molecular distortions on atomic orbitals
USEFUL FOR

Quantum chemists, physicists, and researchers involved in molecular modeling and computational chemistry who are interested in understanding atomic and molecular orbital interactions.

ftft
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I am trying to find a way to calculate the overlap integral between atomic orbitals centred on two different atoms, A & B as a function of the separation distance. I hope someone in the forum can give a hint on how to do that.
Thanks,
ftft
 
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Since orbitals are normally written in spherical polar coordinates, you'll have to convert them into Cartesian coordinates. I assume you know the equations for the spherical harmonics and the radial wavefunction. But the orbitals also get distorted by the presence of the other atom, so it becomes hard.
 
That's a good point Khashishi..
OK.. what if we generalize the problem to two molecules, A & B? each will then have molecular orbitals made by LCAO. To measure overlap in this case: Do we use the Slater wave function (which is determinant of LCAOs including occupied and empty orbitals) for each molecule? Or is it enough to compose the wave function from occupied orbitals? Mathematically, is it enough to calculate the inner product of the two (chosen) wave functions? I am assuming that only those parts of the two wave functions which see each other will contribute to the overlap integral.. how mathematically can we restrict the overlap a small part of the wave functions?
 

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